Subgroups — #14415848

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91796	C₂	1	2	yes	maximal, complemented
2	#11756236	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751230	C₂	1	2	yes	maximal, complemented
5	C₂×C₄⋊(C₃⋊#168)	C₂	1	1	yes	maximal, characteristic, complemented
6	#11750807	C₂	1	4	yes	maximal, complemented
7	#11750789	C₂	1	2	yes	maximal, complemented
8	C₈×D₆₀	C₂	1	2	yes	maximal, complemented
9	#10610253	—	3	1	no	maximal, Hall
10	C₂×#6817	C₂²	1	2	yes	—
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	#91819	C₄	1	2	yes	—
15	#91819	C₄	1	2	yes	—
16	C₂²×C₃⋊#168	C₂²	1	2	yes	—
17	#91796	—	2	8	no	—
18	C₂×#6705	C₂²	1	4	yes	—
19	C₂×C₈×D₁₅	C₂²	1	4	yes	—
20	#91764	C₄	1	2	yes	—
21	#91763	C₄	1	1	yes	characteristic
22	C₄×D₆₀	C₂²	1	2	yes	—
23	C₄×D₆₀	C₂²	1	2	yes	—
24	#91758	C₄	1	1	yes	characteristic
25	C₃×C₅×#97	C₂²	1	2	yes	—
26	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
27	#91104	C₂²	1	4	yes	—
28	#91104	C₂²	1	4	yes	—
29	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
30	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
31	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
32	#78522	—	5	1	no	maximal, Hall
33	C₂×#4053	—	3	2	no	—
34	#65811	—	3	1	no	—
35	C₄×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
36	#65418	—	3	2	no	—
37	C₂×C₄⋊#168	—	3	1	no	—
38	#64995	—	3	4	no	—
39	#64977	—	3	2	no	—
40	C₈×D₂₀	—	3	2	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂×#1220	C₂×C₄	1	4	yes	—
45	#6817	—	2	4	no	—
46	#6817	—	2	4	no	—
47	C₂×D₆₀	C₂×C₄	1	2	yes	—
48	C₂×D₆₀	C₂×C₄	1	2	yes	—
49	C₂×D₆₀	C₂×C₄	1	2	yes	—
50	C₂×C₄×D₁₅	C₂³	1	4	yes	—
51	C₂×Dic₃₀	C₂×C₄	1	2	yes	—
52	C₃×C₅×M₁₆	—	2	2	no	—
53	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
54	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
55	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
56	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
57	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
58	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
59	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
60	#6714	C₂×C₄	1	4	yes	—
61	#6714	C₂×C₄	1	4	yes	—
62	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
63	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
64	C₂×C₃⋊#168	—	2	4	no	—
65	C₂×C₃⋊#168	C₂³	1	2	yes	—
66	C₂×C₃⋊#168	C₂³	1	2	yes	—
67	#6705	—	2	8	no	—
68	C₈×D₁₅	—	2	8	no	—
69	C₂×#907	—	5	2	no	—
70	#5477	—	5	1	no	—
71	C₃×C₄×M₁₆	D₅	1	1	yes	characteristic, complemented
72	#5129	—	5	2	no	—
73	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
74	#4706	—	5	4	no	—
75	#4688	—	5	2	no	—
76	C₈×D₁₂	—	5	2	no	—
77	C₂×#709	—	3	2	no	—
78	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
79	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
81	#4076	—	3	2	no	—
82	#4076	—	3	2	no	—
83	C₂²×#168	—	3	2	no	—
84	#4053	—	6	8	no	—
85	C₂×#676	—	3	4	no	—
86	C₂×C₈×D₅	—	3	4	no	—
87	#4021	—	3	2	no	—
88	#4020	—	3	1	no	—
89	C₄×D₂₀	—	3	2	no	—
90	C₄×D₂₀	—	3	2	no	—
91	#4015	—	3	1	no	—
92	C₅×#97	C₂×D₃	1	2	yes	—
93	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
94	#3952	—	3	4	no	—
95	#3952	—	3	4	no	—
96	C₄⋊#168	—	3	1	no	—
97	C₄⋊#168	—	3	1	no	—
98	C₄⋊#168	—	3	2	no	—
99	#2935	—	15	1	no	Sylow
100	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂²×D₁₅	C₂²×C₄	1	4	yes	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	#41	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	#1220	—	2	8	no	—
113	C₂×Dic₁₅	C₂²×C₄	1	4	yes	—
114	D₆₀	—	2	4	no	—
115	D₆₀	—	2	4	no	—
116	D₆₀	—	4	2	no	—
117	C₄×D₁₅	—	2	4	no	—
118	C₄×D₁₅	—	2	4	no	—
119	Dic₃₀	—	2	4	no	—
120	C₃×C₅×C₈	—	2	2	no	—
121	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
122	C₃⋊#168	—	2	2	no	—
123	C₃⋊#168	—	2	2	no	—
124	C₂×#235	—	5	2	no	—
125	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
126	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
127	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
128	#930	—	5	2	no	—
129	#930	—	5	2	no	—
130	C₂²×C₃⋊C₈	—	5	2	no	—
131	#907	—	10	8	no	—
132	C₂×ΓL(1,𝔽₂₅)	—	5	4	no	—
133	C₂×D₃×C₈	—	5	4	no	—
134	#875	—	5	2	no	—
135	#874	—	5	1	no	—
136	C₄×D₁₂	—	5	2	no	—
137	C₄×D₁₂	—	5	2	no	—
138	#869	—	5	1	no	—
139	C₃×#97	C₂×D₅	1	2	yes	—
140	C₃×C₄×C₈	C₂×D₅	1	2	yes	—
141	(C₂×D₃)⋊C₈	—	5	4	no	—
142	(C₂×D₃)⋊C₈	—	5	4	no	—
143	C₄⋊(C₃⋊C₈)	—	5	1	no	—
144	C₄⋊(C₃⋊C₈)	—	5	1	no	—
145	C₄⋊(C₃⋊C₈)	—	5	2	no	—
146	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
149	C₂×C₂²⋊D₅	—	3	4	no	—
150	#709	—	6	4	no	—
151	#709	—	6	4	no	—
152	C₂×D₂₀	—	3	2	no	—
153	C₂×D₂₀	—	3	2	no	—
154	C₂×D₂₀	—	3	2	no	—
155	C₂×C₄×D₅	—	3	4	no	—
156	C₂×Dic₁₀	—	3	2	no	—
157	C₅×M₁₆	—	2	2	no	—
158	C₅×M₁₆	D₁₂	1	4	yes	complemented
159	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
160	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
161	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
162	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
163	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
164	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
165	#685	—	3	4	no	—
166	#685	—	3	4	no	—
167	C₄⋊Dic₅	—	3	2	no	—
168	C₄⋊Dic₅	—	3	2	no	—
169	C₂×#168	—	3	2	no	—
170	C₂×#168	—	3	2	no	—
171	C₂×#168	—	6	4	no	—
172	#676	—	6	8	no	—
173	C₈×D₅	—	6	8	no	—
174	C₂×#131	—	15	2	no	—
175	#532	—	15	1	no	—
176	#436	—	15	2	no	—
177	#435	—	15	4	no	—
178	C₈×D₄	—	15	2	no	—
179	C₂×C₄⋊C₈	—	15	1	no	—
180	#408	—	15	2	no	—
181	C₄×M₁₆	D₁₅	1	1	yes	characteristic, complemented
182	C₂²×C₃×C₅	—	2	1	no	—
183	C₂²×C₃×C₅	—	2	1	no	—
184	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
185	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
186	C₂×D₁₅	—	2	4	no	—
187	C₂×D₁₅	—	2	4	no	—
188	C₂×D₁₅	—	2	4	no	—
189	C₃×C₄×C₅	—	2	1	no	—
190	C₃×C₄×C₅	—	2	1	no	—
191	C₃×C₄×C₅	—	2	1	no	—
192	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
193	C₃×C₄×C₅	#131	1	2	yes	complemented
194	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
196	Dic₁₅	—	2	4	no	—
197	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
198	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
200	C₂×#67	—	5	4	no	—
201	#235	—	10	4	no	—
202	#235	—	10	4	no	—
203	C₂×D₁₂	—	5	2	no	—
204	C₂×D₁₂	—	5	2	no	—
205	C₂×D₁₂	—	5	2	no	—
206	C₂×C₄×D₃	—	5	4	no	—
207	C₂×Dic₆	—	5	2	no	—
208	C₃×M₁₆	—	2	2	no	—
209	C₃×M₁₆	D₂₀	1	4	yes	complemented
210	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
211	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
212	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
213	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
214	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
215	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
216	(C₂×D₃)⋊C₄	—	5	4	no	—
217	(C₂×D₃)⋊C₄	—	5	4	no	—
218	C₄⋊Dic₃	—	5	2	no	—
219	C₄⋊Dic₃	—	5	2	no	—
220	C₂×C₃⋊C₈	—	5	2	no	—
221	C₂×C₃⋊C₈	—	5	2	no	—
222	C₂×C₃⋊C₈	—	10	4	no	—
223	ΓL(1,𝔽₂₅)	—	10	8	no	—
224	D₃×C₈	—	10	8	no	—
225	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
226	C₂²×D₅	—	3	4	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	4	1	no	—
229	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
235	C₂×C₄×C₅	#235	1	2	yes	—
236	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
237	C₂²⋊D₅	—	6	8	no	—
238	C₂×Dic₅	—	3	4	no	—
239	D₂₀	—	6	4	no	—
240	D₂₀	—	6	4	no	—
241	D₂₀	—	12	2	no	—
242	C₄×D₅	—	6	4	no	—
243	C₄×D₅	—	6	4	no	—
244	Dic₁₀	—	6	4	no	—
245	C₅×C₈	—	2	2	no	—
246	C₅×C₈	C₂×D₁₂	1	4	yes	—
247	#168	—	6	2	no	—
248	#168	—	6	2	no	—
249	C₂×#41	—	15	2	no	—
250	#131	—	30	8	no	—
251	C₂×M₁₆	—	15	4	no	—
252	C₂×M₁₆	C₂×D₁₅	1	1	yes	characteristic
253	C₂×M₁₆	C₂×D₁₅	1	1	yes	characteristic
254	C₂²×C₈	—	15	2	no	—
255	C₂²×C₈	—	15	4	no	—
256	C₄⋊Q₈	—	15	1	no	—
257	#127	—	15	1	no	—
258	#124	—	15	2	no	—
259	#121	—	15	2	no	—
260	#121	—	15	2	no	—
261	C₄×D₄	—	15	2	no	—
262	C₄×D₄	—	15	2	no	—
263	C₂×C₄²	C₂×D₁₅	1	1	yes	characteristic
264	C₄⋊C₈	—	15	1	no	—
265	C₄⋊C₈	—	15	2	no	—
266	C₄⋊C₈	—	15	1	no	—
267	C₂²⋊C₈	—	15	4	no	—
268	C₂²⋊C₈	—	15	4	no	—
269	#97	C₂×D₁₅	1	2	yes	—
270	C₄×C₈	C₂×D₁₅	1	2	yes	—
271	C₂×C₃×C₅	—	2	2	no	—
272	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
274	C₂×C₃×C₅	#568	1	1	yes	characteristic
275	D₁₅	—	4	4	no	—
276	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
277	C₂²×D₃	—	5	4	no	—
278	C₂×C₃×C₄	—	2	2	no	—
279	C₂×C₃×C₄	—	4	1	no	—
280	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
286	C₂×C₃×C₄	#709	1	2	yes	—
287	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
288	#67	—	10	8	no	—
289	C₂×Dic₃	—	5	4	no	—
290	D₁₂	—	10	4	no	—
291	D₁₂	—	10	4	no	—
292	D₁₂	—	20	2	no	—
293	C₄×D₃	—	10	4	no	—
294	C₄×D₃	—	10	4	no	—
295	Dic₆	—	10	4	no	—
296	C₃×C₈	—	2	2	no	—
297	C₃×C₈	C₂×D₂₀	1	4	yes	—
298	C₃⋊C₈	—	10	2	no	—
299	C₃⋊C₈	—	10	2	no	—
300	C₂²×C₅	—	2	1	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	C₄×D₁₂	1	2	yes	—
303	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
304	C₂×D₅	—	6	4	no	—
305	C₂×D₅	—	6	4	no	—
306	C₂×D₅	—	6	4	no	—
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	C₄×D₁₂	1	2	yes	—
311	C₄×C₅	#907	1	2	yes	complemented
312	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
313	C₄×C₅	C₂×#235	1	1	yes	characteristic
314	Dic₅	—	6	4	no	—
315	#41	—	30	4	no	—
316	#41	—	30	4	no	—
317	C₂×Q₈	—	15	2	no	—
318	C₂×D₄	—	15	4	no	—
319	C₂×D₄	—	15	2	no	—
320	C₂×D₄	—	15	2	no	—
321	C₂×D₄	—	15	2	no	—
322	C₂²×C₄	—	15	4	no	—
323	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
324	C₂²×C₄	C₄×D₁₅	1	1	yes	characteristic
325	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
326	M₁₆	—	2	2	no	—
327	M₁₆	—	30	8	no	—
328	M₁₆	D₆₀	1	4	yes	complemented
329	C₂×C₈	—	15	2	no	—
330	C₂×C₈	—	15	2	no	—
331	C₂×C₈	—	30	4	no	—
332	C₂×C₈	—	30	8	no	—
333	C₂×C₈	C₂²×D₁₅	1	2	yes	—
334	C₂×C₈	C₂²×D₁₅	1	2	yes	—
335	C₄⋊C₄	—	15	2	no	—
336	C₄⋊C₄	—	15	2	no	—
337	C₂²⋊C₄	—	15	4	no	—
338	C₂²⋊C₄	—	15	4	no	—
339	C₄²	C₄×D₁₅	1	1	yes	characteristic
340	C₄²	C₄×D₁₅	1	1	yes	characteristic
341	C₄²	C₂²×D₁₅	1	1	yes	characteristic
342	C₄²	C₂²×D₁₅	1	1	yes	characteristic
343	C₃×C₅	#2935	1	1	yes	characteristic, complemented, Hall
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	2	1	no	—
346	C₂²×C₃	C₄×D₂₀	1	2	yes	—
347	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
348	C₂×D₃	—	10	4	no	—
349	C₂×D₃	—	10	4	no	—
350	C₂×D₃	—	10	4	no	—
351	C₃×C₄	—	2	1	no	—
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	C₄×D₂₀	1	2	yes	—
355	C₃×C₄	#4053	1	2	yes	complemented
356	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
357	C₃×C₄	C₂×#709	1	1	yes	characteristic
358	Dic₃	—	10	4	no	—
359	C₂×C₅	—	2	2	no	—
360	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
361	C₂×C₅	C₂×#907	1	1	yes	characteristic
362	C₂×C₅	#5745	1	1	yes	characteristic
363	D₅	—	12	4	no	—
364	C₂³	—	15	4	no	—
365	C₂³	C₂×C₄×D₁₅	1	1	yes	characteristic
366	Q₈	—	30	4	no	—
367	D₄	—	30	8	no	—
368	D₄	—	30	4	no	—
369	D₄	—	30	4	no	—
370	D₄	—	60	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	15	4	no	—
374	C₂×C₄	—	30	4	no	—
375	C₂×C₄	—	30	4	no	—
376	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
377	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
378	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
379	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
380	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
381	C₂×C₄	C₂×D₆₀	1	2	yes	—
382	C₂×C₄	#6817	1	2	yes	—
383	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
384	C₈	—	2	2	no	—
385	C₈	—	30	2	no	—
386	C₈	—	30	2	no	—
387	C₈	C₂×D₆₀	1	4	yes	—
388	C₂×C₃	—	2	2	no	—
389	C₂×C₃	C₂×C₄×D₂₀	1	1	yes	characteristic
390	C₂×C₃	C₂×#4053	1	1	yes	characteristic
391	C₂×C₃	#66079	1	1	yes	characteristic
392	D₃	—	20	4	no	—
393	C₅	#78522	1	1	yes	characteristic, complemented, Sylow
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	30	4	no	—
397	C₂²	—	30	4	no	—
398	C₂²	—	30	4	no	—
399	C₂²	C₄×D₆₀	1	2	yes	—
400	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	30	4	no	—
405	C₄	C₄×D₆₀	1	2	yes	—
406	C₄	#91796	1	2	yes	complemented
407	C₄	C₂²×D₆₀	1	1	yes	characteristic
408	C₄	C₂×#6817	1	1	yes	characteristic
409	C₃	#10610253	1	1	yes	characteristic, complemented, Sylow
410	C₂	—	2	2	no	—
411	C₂	—	60	4	no	—
412	C₂	C₂×C₄×D₆₀	1	1	yes	characteristic
413	C₂	C₂×#91796	1	1	yes	characteristic
414	C₂	#11756504	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₄×C₅×M₁₆	C₂
prime radical	#11756236	C₂
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×M₁₆	D₁₅
hypocenter	C₃×C₅	#2935
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#91796	C₂	semidirect
3. C₃×C₄×C₅×M₁₆	C₂	semidirect
4. #11751230	C₂	semidirect
5. C₂×C₄⋊(C₃⋊#168)	C₂	semidirect
6. #11750807	C₂	semidirect
7. #11750789	C₂	semidirect
8. C₈×D₆₀	C₂	semidirect
35. C₄×C₅×M₁₆	D₃	semidirect
53. C₃×C₅×M₁₆	D₄	semidirect
71. C₃×C₄×M₁₆	D₅	semidirect
158. C₅×M₁₆	D₁₂	semidirect
181. C₄×M₁₆	D₁₅	semidirect
193. C₃×C₄×C₅	#131	semidirect
209. C₃×M₁₆	D₂₀	semidirect
311. C₄×C₅	#907	semidirect
328. M₁₆	D₆₀	semidirect
343. C₃×C₅	#2935	semidirect
355. C₃×C₄	#4053	semidirect
393. C₅	#78522	semidirect
406. C₄	#91796	semidirect
409. C₃	#10610253	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#91796	2
#11756236	2
C₃×C₄×C₅×M₁₆	2
#11751230	2
C₂×C₄⋊(C₃⋊#168)	2
#11750807	2
#11750789	2
C₈×D₆₀	2
#10610253	3
#78522	5